Coxter群中二阶元的判定及其在仿射Weyl群中的应用

JUDGEMENT OF AN ELEMENT OF ORDER TWO IN A COXTER GROUP AND ITS APPLICATION TO AFFINE WEYL GROUP

本文首先给出Coxter群中二阶元的判定方法,应用到E_6型有限Weyl群及A_(21)^(1)型仿射Wey1群,给出了其二阶元的共轭标准形与共轭类数.

In this paper, we give a method for judging which elements in the Coxter groups are of order two. As an application, For affine Weyl group of type A2 and finite Weyl group of type E6, we give a conjugacy classification of elements of order two.